Do I need to report my India Salary income?(Jan-Sept 2013)
If it is last paid before you first stepped foot in the US - then no. You only report Indian salary paid after the date you moved to the US.
Do I need to include my India Bank interest income? If yes, do I need
to report entire year interest income or only from Oct to Dec 2013?
Same thing. You only report what's been paid after you moved to the US. However, you report what's paid, not what's accrued, so if you are paid interest in December for the whole year - you report and pay US taxes on all of it, you don't get to prorate.
Do I get a foreign tax credit?
If you paid foreign taxes on income taxable in the US - you can claim foreign tax credit. If you paid taxes on income before you moved to the US - you cannot.
Can I claim for Child Tax credit?
Not for 2013, since you will only be partial year resident. For years where you're a full-year resident - you may qualify depending on the rest of the qualification requirements.
The statute addresses this:
(f) Taxable year must be full taxable year
Except in the case of a taxable year closed by reason of the death of the taxpayer, no credit
shall be allowable under this section in the case of a taxable year
covering a period of less than 12 months.